Nash Equilibrium Approximation in Games of Incomplete Information
by
Armantier Olivier
SUNY Stony Brook
Coauthors: FLORENS Jean-Pierre (IDEI-Universite de Toulouse), RICHARD Jean-Francois (Pittsburgh University)

The most commonly used solution concept in game theory is that of (bayesian)Nash Equilibrium (NE).However, except under fairly restrictive assumptions whose empirical validity often is questionable, many games cannot be solved analytically for NE solutions. As an alternative to NE Armantier, Florens and Richard introduce the concept of Constrained Strategic Equilibrium (hereafter CSE). Essentially, they propose to restrict attention to appropriate subsets of strategies, typically indexed by an auxiliary parameter vector, and to search for an equilibrium solution within such subsets. The authors show that CSE offer a major computational advantage, and they provide a powerful algorithm based upon Monte Carlo simulations to determine the CSE numerically. The concept of CSE appeared to be relevant under two scenarios: the first one is directly related to the general notion of 'bounded rationality' and more specifically to the concept of Rules of Thumb ; in the second scenario, one would use the computational advantage of the CSE with the intent to approximate an analytically untractable NE solution. The objective of the present essay is to establish conditions under which a sequence of CSE approximates a NE, in the context of games of incomplete information. We also provide three criteria to document in practice whether the CSE is a good approximation of the NE and how far the CSE is from a NE.

Date received: July 24, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cafl-46.